A158608 a(n) = a(n-1) + 16*a(n-2), starting a(0)=1, a(1)=4.

1, 4, 20, 84, 404, 1748, 8212, 36180, 167572, 746452, 3427604, 15370836, 70212500, 316145876, 1439545876, 6497879892, 29530613908, 133496692180, 605986514708, 2741933589588, 12437717824916, 56308655258324, 255312140456980

Offset: 0

Author

Roger L. Bagula, Mar 22 2009

Keywords

• nonn
• easy

Comments

Quadratic equation associated with group [3,3,5] which instead of t=phi uses t=2 in Phi(t) = (1 + sqrt(1+4*t^4))/(2*t).

References

• H. S. M. Coxeter, Regular Polytopes, 3rd ed., Dover, NY, 1973, page 221.

Links

• Index entries for linear recurrences with constant coefficients, signature (1,16).

Crossrefs

Cf. A168579.

Programs

Mathematica

Clear[M, v, t, n];
M = {{0, t}, {t, 1/t}};
v[0] = {1, 1};
v[n_] := v[n] = M.v[n - 1];
t = 2;
a = Table[t^n*v[n][[1]], {n, 0, 30}]

Formula

a(n) = A168579(n) + 3*A168579(n-1).

G.f.: (1+3x)/(1-x-16*x^2). - Philippe Deléham, Mar 26 2009

Extensions

Definition simplified following the Deleham proposition of Mar 2009 - The Assoc. Eds. of the OEIS, Aug 29 2010